What Lawrence Summers might have said if he’d studied more math in college.

Should there be more women on mathematics faculty?  Let’s do the math:

I would like everyone here to now consider the following problem. Its solution will tell us more about gender inequity than an infinity of National Bureau of Economic Research conferences.

A random selection of N_M  men and N_W  women compete for N_S  available slots. If the slots are filled in rank order of mathematical ability, what is the most probable gender composition of the winners’ circle?

The solution is obtained simply by requiring that at the end of the selection process the number of slot holders equals the number of slots. That is,

(equation here—I can’t figure out how to format it in Typepad, sorry:)

N_M  times [the integral over x, from L to infinity, of P_M  (x)]     

   + N_W  times [the integral over x, from L to infinity, of  P_W (x)] 

         =  N_S

where P_M  and P_W  are the normalized math-ability distributions of men and women, respectively, and L is the minimum ability needed to secure a slot, i.e., the mathematical ability of the dimmest bulb among the slot holders.

The results seem to show that the proportion of women in the top tier of mathematicians is just about where it ought to be (assuming that the normalized math-ability distributions of men and women are a given, and not something that should or could be altered).

I like math.  I’m one of the 29% of people at the 99th percentile in mathematical ability (well, at age 15 I was anyway) who are women.  But I can relate to this essay, written as "what Summers should have said," especially in the imaginary Q and A session at the end:

Q: If all this is so, why are we meeting here today?

A: Good question. We are meeting here today because feminists, in order to support their androgynous fantasies, encourage able young women to enter technological fields even when their interests lie elsewhere.

H/T The Corner.